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Calculus 151 Regression ProjectPowerPoint Presentation

Calculus 151 Regression Project

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### Calculus 151 Regression Project

Data collected from the NJ Department of Education Website

Sine Regression

Instantaneous Rate of Change at 2003 = -5.174

Quartic RegressionR2 =.555

Instantaneous Rate of Change at 2003 = -1.826

Split Regressions

Limit x 6.5- 75.25657 Limit x 6.5+ 71.669602

Derivatives of exponential, logarithmic, and sine regressions

Y’= 74.56303051 *.9993957215^x *ln(.9993957215)

Y’= -.6345494264

x

Y’=-6.784189065* cos(-2.304469566 x + 1.333706904)

Mean Value Theorem

f’(c) = 75.682- 76.565

11-2

f’(c) = - .883

9

f’(c) = -.098

c = X

f(c) = Y4

f’(c) = Y5

Y= -.098(x – 3.4931) + 71.661

Y= -.098(x – 6.9124) + 75.325

Y= -.098(x – 9.67854) +72.782

Max and Min of Cubic Regression

The Regression has a minimum at 5.4093854 and a maximum at 10.033224. It is increasing between [5.4093854, 10.033224] ,and is decreasing between (- ∞ , 5.4093854) U (10.033224, ∞).

Second derivative of cubic regression

Second Derivative Zero

Inflection Point

Concave up

Concave down

First Derivative Maximum

Approximating area under a curve using left endpoints

Estimate Area is

668.504

72.432

73.684

77.426

74.644

76.352

71.138

76.517

74.42

71.891

Approximating area under a curve using right endpoints

Estimate Area is

670.836

76.352

71.138

76.517

74.42

71.891

77.426

72.432

73.684

76.976

Finding Area under the curve using the Fundamental Theorem of Calculus

11

Area=∫02 2.943926518sin(-2.304469566x+1.333706904) +74.26459702dx

F(x)= 1.277485527cos(-2.304469566x +1.333706904)+74.26459702x

F(11)- F(02)≈ 817.47-147.26≈ 670.21

Area ≈ 670.21

Actual Area under the curve of Calculus

Average Value of Calculus

Area= the sum of the % of students proficient in Mathematics over the past 9 years

Average % of students 670.69193

proficient in Mathematics = 9 ≈ 74.55%

for each year

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